Question

A hydrogen balloon released on the moon would:
A. Climb up with an acceleration of \[98\,{\text{m/se}}{{\text{c}}^2}\]
B. Climb up with an acceleration of \[98 \times 6\,{\text{m/se}}{{\text{c}}^2}\]
C. Neither climb nor fall
D. Fall with an acceleration of \[\left( {9.8/6} \right)\,{\text{m/se}}{{\text{c}}^2}\]

Answer 1

Hint: There are two forces that act on the balloon: gravitational force and buoyant force. The buoyant force acting on the balloon is due to the atmospheric gases providing upward thrust to the balloon. The moon has no atmosphere.

Complete answer:
To answer this question, let’s consider the scenario of hydrogen balloon released in the earth’s atmosphere. There are two forces that act on the balloon: gravitational force and buoyant force. We know that the direction of gravitational force is downwards while the direction of buoyant force is upwards. If we throw a piece of wood in the water, the piece of wood obviously will float in the water. This is because the buoyant force or we can say the density of water is greater than the density of the wood. Thus, when we release the hydrogen balloon in the earth’s atmosphere, the density of hydrogen is less than that of nitrogen and oxygen in the atmosphere. Therefore, eventually, the hydrogen balloon will rise in the atmosphere.

Now, we know that the moon has no atmosphere. Therefore, there are no nitrogen and oxygen gases. Thus, there will not be buoyant force due to the atmosphere acting on the inner hydrogen gas. Now, the net force acting on the hydrogen balloon is only the gravitational force acting on the small mass of the balloon. We know that the acceleration due to gravity of the moon is 6 times less than the acceleration due to gravity of the earth. Therefore, the balloon will descend with acceleration \[\left( {9.8/6} \right)\,{\text{m/se}}{{\text{c}}^2}\].

So, the correct answer is option D.

Note: If the balloon is filled with denser gas than oxygen and nitrogen, the pressure below the balloon will be less than the pressure above the balloon. In that case, the balloon will descend in the earth’s atmosphere. The acceleration gravity on the surface of moon is \[1.625\,{\text{m/se}}{{\text{c}}^2}\] and the acceleration gravity of the surface of earth is \[9.8\,{\text{m/se}}{{\text{c}}^2}\].